A060908 E.g.f.: exp(x*exp(x*exp(x)) + 1/2*x^2*exp(x*exp(x))^2).

1, 1, 4, 25, 194, 1791, 19312, 237637, 3280524, 50136049, 839267936, 15255154179, 298936866736, 6277386102703, 140540145723720, 3339966073612921, 83936496568012208, 2223184658988286113, 61877234830148427808

Offset: 0

Author

Vladeta Jovovic, Apr 07 2001

Keywords

• nonn

Comments

a(n) = the number of functions f:{1,2,...,n} -> {1,2,...,n} such that the functional digraphs have cycle lengths at most 2 and no element is at a distance of more than 2 form a cycle. - Geoffrey Critzer, Sep 23 2012

References

• I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Crossrefs

Cf. A000949-A000951, A060905-A060913.

Programs

Mathematica

nn=20; a=x Exp[x]; b=x Exp[a]; t=Sum[n^(n-1)x^n/n! ,{n, 1, nn}]; Range[0,nn]! CoefficientList[Series[Exp[b+b^2/2], {x, 0, nn}], x]  (* Geoffrey Critzer, Sep 23 2012 *)

Formula

E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 2, m = 2.